US Cavalry scout units did serve in the Phillipines into the 1920s but not armed with Schofields and Trapdoors. I don't think any US Cavalry unit ever charged with sabers after the Civil War did they? Maybe in the Indian wars, but by then we were sold on pistols as the first weapon of choice. You have to remember, the United States did not have a huge Cavalry tradition prior to the Civil war and not much after. In Europe, elite cavalry units existed for centuries and they had a hard time getting rid of those traditions since they were often populated by the aristocracy and families had generational ties to units. I think one of the first, if not the first, British confirmed kills in WWI was a Cavalryman against a German Uhlan (using a new pattern saber). The Soviets used Cavalry in the second war for recon as I recall, and as kind of a weird, fast infantry (fighting dismounted) but not on a large scale.
This thread got me going and casting around on the web I read the following though I cannot vouch for its accuracy it is interesting as it pertains to US mounted troops:
The last horse cavalry charge by an Army cavalry unit took place against Japanese forces during the fighting in the Bataan Peninsula, Philippines, in the village of Morong on 16 January 1942, by the 26th Cavalry Regiment of the Philippine Scouts. Shortly thereafter, the besieged combined United States-Philippine forces were forced to slaughter their horses for food and the 26th Regiment fought on foot or in whatever scarce vehicles were available until their surrender.
The 10th Mountain Cavalry Reconnaissance Troop of the 10th Mountain Division, while not designated as U.S. Cavalry, conducted the last horse-mounted charge of any Army organization while engaged in Austria in 1945.[6] An impromptu pistol charge by the Third Platoon was carried out when the Troop encountered a machine gun nest in an Italian village/town sometime between 14–23 April 1945.
The last Cavalry unit I remember was a South African unit that worked on horseback and did as a matter of course have one mounted charge before apartheid was overthrown, but it has been years since I read about them.